The present invention generally relates to methods of signal processing for improved spectral reconstruction, and more particularly to algorithmic methods for conditioning and deconvolving a spectral image to compensate for non-ideal behavior in a static multimode spectrometer.
An exemplary spectrometer for static Multimodal Multiplex Spectrometry (MMS) is described in U.S. application Ser. No. 11/334,546, filed Jan. 19, 2006, which is herein incorporated by reference. “Static” refers to the lack of mechanical, electro-optical or other active modulation in reconstructing the optical spectrum.
In present applications of static MMS, the imaging of an aperture through a dispersion system, e.g., a diffraction grating, results in an image that is curved in the direction of the dispersion (i.e., so called smile distortion). Assuming that the curvature is corrected or is negligible, accurate mathematical reconstruction of the spectral content relies on several key assumptions: 1) the propagation kernel is free from distortion, 2) the system input is a diffuse light source that has uniform intensity in the x and y directions, and 3) the detector resolution is higher than that of the mask elements. These assumptions were noted in Gehm et al., “Static 2D aperture coding for multimodal multiplex spectroscopy,” Appl. Opt. 45(13) 2965-74, May, 2006. In addition, accurate mathematical reconstruction of the spectral content relies on the assumption that the dispersion system does not cause nonlinear dispersion in the spectrometer.
These assumptions may be problematic because some propagation kernels may behave non-ideally, because certain diffuse sources, such as liquids, may provide non-uniform illumination of the coded aperture, and because dispersion systems may disperse light in a nonlinear. Simple spectral reconstruction using the conventional methods may therefore introduce spectral artifacts in the reconstructed optical spectrum.